Multiplicity upon restriction to the derived subgroup

Jeffrey D. Adler and Dipendra Prasad

Vol. 301 (2019), No. 1, 1–14

DOI: 10.2140/pjm.2019.301.1

Abstract

We present a conjecture on multiplicity of irreducible representations of a subgroup $H$ contained in the irreducible representations of a group $G$, with $G$ and $H$ having the same derived groups. We point out some consequences of the conjecture, and verification of some of the consequences. We give an explicit example of multiplicity $2$ upon restriction, as well as certain theorems in the context of classical groups where the multiplicity is $1$.

Keywords

reductive group, derived subgroup, representation, restriction, multiplicity

Mathematical Subject Classification 2010

Primary: 22E50

Milestones

Received: 10 June 2018

Accepted: 5 September 2018

Published: 16 September 2019